Radical Expressions
Operations with Radical Expressions
Please review the additional presentations for operations with radical numbers. There are extra links if you need more help. In this class we use the same concepts to perform operations with complex numbers.
You should begin to understand that when a radicand is greater than or equal to zero, the numbers are from the set of real numbers and when a radicand is less than zero, the numbers are from the set of complex numbers. Complex numbers have a special form:
a + bi
a is the real number part and the bi is the imaginary number. Complex numbers of this form have applications in electricity and vectors, which are objects in motion. All real numbers are also complex numbers and could be written in the form of a + 0i.
Imaginary numbers could be written 0 + bi.
Simplifying Imaginary Numbers
We simplify imaginary numbers in the same manner as other radicals after doing one thing first, taking the i out. Look at the following.
Example: √-4
Simplify
=√-1 x √4 it could be written this way. Why We factored -4 to -1 x 4 so that we could remove the i! ?
= i x 2 then simplify 4 = 22, so the square root of 4 is 2.
= 2i commutative property
Examples
Simplify √-12.
= √ * √-12
= √-1 * √-12
= * √4 * 3
= i * 2 √
= i * 2 √3
= √
Simplify √-24x4y7
=√ * √-24x4y7
√-1 * √-24x4y7
= * √-24x4y7
= i * √-24x4y7
= i * √ * 64y6y1
= i * √4i * 64y6y1
= x2y3√
